You are the owner/ manager of a small competitive firm that manufactures house paints. You and all your 1000 competitors have total cost curves given by

TC = 8 + 2Q + 2Q2,

And the industry is in long- run equilibrium. Now you are approached by an inventor who holds a patent on a process that will reduce your costs by half at each level of output.
a. What is the most you would be willing to pay for the exclusive right to use this invention?
b. Would the inventor be willing to sell at that price?